One single-particle reconstruction technique is the reconstruction of macromolecules from projection images of randomly oriented particles (SPRR). In SPRR the reliability and consequent interpretation of the final reconstruction is affected by errors arising from incorrect assignment of projection angles to individual particles. In order to improve the resolution of SPRR we studied the influence of imperfect assignment on 3D blurring. We find that this blurring can be described as a Point Spread Function (PSF) that depends on the distance from geometrical center of the reconstructed volume and that blurring is higher at the periphery. This particular PSF can be described by an almost pure tangential angular function with a negligible radial component. We have developed a reliable algorithm for spherical deconvolution of the 3D reconstruction. This spherical deconvolution operation was tested on reconstructions of GroEL and mitochondrial ribosomes. We show that spherical deconvolution improves the quality of SPRR by reducing blurring and enhancing high frequency components, particularly near the periphery of the reconstruction. (C) 2014 Elsevier Inc. All rights reserved.